We were getting the Duplicate Column Heading Existing while trying to download template for data import for Opportunity Entity.
Through Customizations we changed the Display Name of the fields that were duplicate and it fixed the issue for us.
I had the same issue. In Settings> Customizations, display the Entities that causes the error. Sort the fields by display name and scroll through the list until you find two identical display names. Rename one, save and publish your changes. You should now be able to download the Import template.
Do check out this awesome article
Hope it helps ..